"Today, Leader Reid and I are introducing legislation that suspends the debt limit, avoiding default. The bill mirrors legislation we passed earlier this year and will suspend the debt limit until Dec. 31, 2014, after the mid-term elections," the Montana Democrat said. "On Jan. 1, 2015, a new debt limit is set which reflects whatever borrowing is done between passage of the bill and Dec. 31, 2014."

The Senate's expected to take a first procedural vote on the "clean" measure by week's end.

The remarks from Baucus came during a series of floor speeches by Democratic and Republican senators that followed Senate Majority Leader Harry Reid's decision to call a rare live quorum to force senators to the floor in order to "initiate an open conversation about the importance" of resolving the federal shutdown and raising the debt limit.

"It is time for senators to stand before the American people and publicly discuss the path forward. Democrats stand before you unified asking the Speaker to reopen the government — the whole government — and not in some piecemeal fashion that further demonstrates to the world that we are unable to find real solutions. Open the whole government so we can get back to work," Reid said. "Allow the government to do its duty by our military families and by every American family. Avert the threat of a catastrophic default on the nation's bills. Then we'll negotiate on anything you want to negotiate."

A number of Democrats have already spoken, including Budget Chairwoman Patty Murray, D-Wash., who made the 20th attempt by Senate Democrats to get unanimous consent for a budget conference. She faced objection from Budget ranking member Jeff Sessions, R-Ala.

Republican Leader Mitch McConnell of Kentucky and Sen. John McCain, R-Ariz., also received consent to speak, with other Republicans joining in as well. Under an agreement, the two parties are alternating.

Though the quorum is mostly for show, bringing everyone to the floor at least for a few minutes could constitute the most talking across party lines that's happened in the Senate in days. Many of the speeches came while most attention was on the White House, where President Barack Obama held a rare news conference.